A machine tool, that is a machine for machining a workpiece with a machining member, typically includes a bed, a column and a head. The workpiece is supported on a worktable which is in turn mounted on the bed. The column vertically extends upwardly from the bed. One or two arms may extend horizontally from the column which may carry the machine head at an upper region thereof. The tool may be securely supported by a tool holder which depends from the machine head or may be supported by guides arranged on the arms. These members which directly or indirectly support a work element, e.g. a machining electrode or the workpiece, are typically composed of a metal or alloy and are subject to thermal deformation or deflection. It has already been recognized that the thermal deflection of these members occur, due to development of heat in the machining zone of the tool in machining engagement with the workpiece and also where driving motors are located, and results in an error in the positions of the work elements. While the possible positioning error which may result from the thermal deflection of these members are typically of the order of micrometers, it has been found that it is not negligible where the machine tool is designed for high-precision machining operations. In an attempt to overcome the thermal deflection of such a member, a coolant may be circulated in contact with the member in the operation of the machine tool. It has been found, however, that this measure simply cannot satisfactorily remove the problem of mispositioning of the work element due to thermal deflection of the supporting member. The mispositioning is especially notable with a machine tool of the electroerosion or electrical machining type where no appreciable external force or mechanical pressure is applied across the tool and the workpiece. It has now been found that changes in heat-emitting characteristics of various heat sources which develop in the course of an operation of the machine tool and changes in temperature of the environment of the machine tool must be taken into account.